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chris_0101

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I am currently in University and I am retaking a course that I dropped last year due to the fact that there was no textbook and the time I spent in the course was a frantic scramble for reliable information and attempting to understand what the professor was teaching. I have looked before and the only textbook that I found that was remotely close to the material that is covered in the course is Multivariable Calculus by Edwards and Penney. I am asking the community for any suggestions for textbooks that cover most, if not all of the topics listed below:

- Differentiation in Several Variables

Partial derivatives, directional derivatives, del operator, Mean-value theorem for a function of several variables, differentiation through an integral, Leibniz's Rule 2nd order derivatives and Clairaut's theorem, Hessian Matrix. Functions from several variables to several variables, Jacobian Matrix

- Inverse - and Implicit functions in several variables

Inverse function theorem

Implicit function theorem

- Quadratic forms

Matrix Representation

Change of variable & diagonalization by congruence

Positive & Negative definiteness, Semi-definieness, determinantal criteria

Sylvester's Theorem

- Extrema

Local extrema-critical points, local max, local min, saddle points, determinantal tests on the Hessian Matrix

Global extrema-existence for continuous functwions on closed, bounded sets, finiding constrained extrema by the method of Lagrange multipliers

- Curves and Surfaces

Space curves defined parametrically-tangent, normal, binormal, arc length, curvature, torsion

Surfaces-implicit and parametric definitions-tangent plane, normal line

Space curves defined as intersecting surgaces, related quadratic & cubic forms

- Integration in several Variables

Multiple and iterated integrals

Change of order of variables

Change of variable formula in general

Polar, cylindrical & spherical coordinates

Line integrals, consecutive and non-consecutive vector fields, curl operator

Surface integrals, projection onto a plane, parametric surgace integrals

Stokes' theorem, boundary curve, orientation

Gauss' theorem, boundary surgace, div operator

Any suggestions will be greatly appreciated and sorry for the long list, I didn't want to leave anything out.